Radar system and method for determining target points on projectile trajectories



c. R. CLEMENCE ETAL 3,182,317 RADAR SYSTEM AND METHOD FOR DETERMINING TARGET May 4, 1965 POINTS 0N PROJECTILE TRAJECTORIES l1 Sheets-Sheet 1 Filed April 1, 1963 ay 1965 c. R. CLEMENCE ETAL 3,132,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET PQINTS UN PROJECTILE TRAJECTORIES Flled April 1, 1963 11 Sheets-Sheet 2 M y 1965 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJEGTILE TRAJECTORIES l1 Sheets-Sheet 3 Filed April 1, 1963 May 4, 1965 C. R. CLEMENCE ETAL RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE TRAJEGTORIES Filed April 1, 1963 11 Sheets-Sheet 4 M y 1965 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE TRAJECTORIES Filed April 1, 1963 ll Sheets-Sheet 5 AIM/f ,ZDAXMP P/W/ (Ma- 4% H5 (F r/a l /a 1965 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE TRAJEC'I'ORIES ll Sheets-Sheet 6 Filed April 1, 1963 M y 1965 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE TRAJECTORIES Filed April 1, 1963 11 Sheets-Sheet 7 [OM10 MW [12 0/ {1 #5 F11; x @QT H 1 T n" L J; Ma I 1 1 y L Z LJ 3 1965 c R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE 'IIMJEC'IORIES Filed April 1, 1965 ll Sheets-Sheet 8 KIA/2 #5 w" g? i- 00 U 7151 May 4, 1965 c. R. CLEMENCE ETAL 3,132,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE THAJECTORIES Filed April 1, 1963 ll Sheets-Sheet 9 .09 .721? Ly if/QQ 44/0 MP? $9325? mw I WWW/Z4 Win g w; @16 n M y 4, 1955 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS 0N PROJECTILE TRAJECTORIES Filed April 1, 1963 ll Sheets-Sheet 10 May 1965 c. R. CLEMENCE ETAL 3,182,317

RADAR SYSTEM AND METHOD FOR DETERMINING TARGET POINTS ON PROJECTILE TRAJECTORIES Filed April 1, 1963 ll Sheets-Sheet 11 I (Ii l f; (152M 722 mm (7/! H37 7 5 Q} l (47% a? Iii [/5 United States Patent Ofi lice 3,182,317 Patented May 4, 1965 59, 11 Claims. (Cl. 343-7) This invention relates to a radar system and method, for use in locating enemy weapons (such as mortars) by obtaining echoes from the projectiles fired by such weapons.

The invention is concerned with a radar system for determining at least two points through which a projectile passes, and including a computer for determining the point of intersection of the trajectory of the projectile with the ground from two of such determined points. When desired for greater accuracy, the time interval required for passage of the projectile between said two points is inserted into the computer. Such a system is of particular utility when the weapon is hidden from direct visual or radar observation.

The radar system is equally useful for watching friendly projectiles aimed at the enemy weapon and for determining the points of impact or burst of such friendly projectiles by making the same extrapolation on the tra jectory of a falling projectile as for a rising projectile. The point on the ground through which such trajectory extends (whether for a rising or falling projectile) is called the target point. In the general case, the target point" is the point of intersection of the projectile trajectory with a selected plane referred to as the working plane. The Working plane is defined as the one including the line between the radar system and the target point and all horizontal lines perpendicular to said line. The angle of the working plane will generally be chosen to give a ground location for the target point, unless tactics otherwise demand.

As already mentioned, the radar system is capable of determining both the location of an enemy weapon and the point of impact of a friendly projectile aimed at such a weapon. An important further feature of the present invention is the provision of a radar system that, in addition to computing the point of impact of the friendly projectile, will calculate the corrections needed to make such point of impact coincide with the position of the enemy weapon.

To this end, the radar system of the invention comprises (a) Means for emitting two closely vertically superposed, mutually divergent, generally horizontal, effectively continuous upper and lower radar beams,

(11) Means for displaying echoes returned by a projectile travelling in either direction in a trajectory intersecting said upper and lower beams and for determining range and azimuth values of such intersection measured from the radar system in relation to a known azimuth datum,

(c) A computer,

(d) Means for supplying the computer with said determined range and azimuth values and with the values of the angles each of said upper and lower beams makes with the horizontal and with the value of the angle a working plane makes with the horizontal,

(e) Said computer including means for calculating at least approximately coordinates of a target point on said working plane through which such trajectory extends,

(f) Means for storing said coordinates,

(g) And means for displaying any diiferences between said stored coordinates and the subsequently derived c0- ordinates of another target point.

The invention also has a method aspect which can be defined in its broad scope as a method of determining the differences between the coordinates of two target points that are each at the respective point of intersection of a. working plane and the trajectory of a projectile, comprising (a) Emitting from a radar system two closely vertically superposed, mutually divergent, generally horizontal, effectively continuous, upper and lower radar beams to intersect the trajectory of a first said projectile,

(b) Determining the angle (0) the lower beam makes with the horizontal, and the angle (or) between the upper and lower beams,

(0) Estimating the angle (qb) made with the horizontal by the line lying in the Working plane and extending from the target point of said first projectiles trajectory to the radar system,

(d) Displaying on a range-azimuth radar display echoes returned by said first projectile during intersection of said upper and lower beams,

(e) Employing the difference in range and azimuth of the intersections so displayed, together with the values of said angles, to determine coordinates of the first target point,

(f) Storing said coordinates,

(g) Repeating steps (a) to (e) for the second pro jcctile to determine the corresponding coordinates of the second target point,

(11) And determining and displaying the differences between the respective coordinates of said target points.

If, however, the coordinates of the first target point are known (the friendly gunners wish to direct their fire onto a given map reference point whether an enemy weapon is firing from such point or not), such known coordinates may be set by the operator on the radar system and the beams and computer employed only to watch friendly projectiles and calculate their points of impact. The coordinates of each point of impact will then be compared in the same manner as before with the coordinates already inserted in the computer.

Details of the extrapolation equations employed and their manner of solution appear from the specific description which follows and which together with the accompanying drawings illustrates one manner in which the invention may be carried into practice. It is to be understood that the radar system specifically illustrated in the drawings and the method of operation described in relation thereto is furnished by way of example of the invention only, the broad scope of the invention being limited only by the appended claims.

In the drawings:

FIGURE 1 is a general perspective view of a radar system according to the invention in operation.

FIGURE 2 is a first diagram of a typical projectile trajectory,

FIGURE 3 is a further diagram of another projectile trajectory,

FIGURE 4 is a plan view of the diagram of FIGURE 3, also showing the position of the radar system,

FIGURE 5 is another diagram provided to illustrate the geometry of the computations,

FIGURE 6a is a plan view of the area scanned by the radar system,

FIGURE 6b demonstrates the manner of presenting such area of scan (FIGURE 6a) on a radar B-scope during a long range searching sweep,

FIGURE 60 shows a portion of the presentation of FIGURE 6b enlarged as it appears for a short range sweep.

FIGURE 7a is a simplified front view of a portion of the radar control panel illustrating diagrammatically the appearance of an echo of a projectile on the screen,

FIGURE 71) is another view similar to FIGURE 70, a short time later in operation,

FIGURE 70 is yet another view similar to FIGURES 7a and 71) at a later stage,

FIGURE 7d is another similar view at yet a later stage in the radar observance of a projectile,

FIGURE 7e is a view similar to FIGURES 7a to d showing the marks made by the operator after the projectile echoes have faded and the manner of use of a marker spot,

FIGURE 7 is a view similar to FIGURE 7e at a later stage in operation,

FIGURE 8 is a general overall circuit for the radar system,

FIGURE 9 is a more detailed illustration of the portion of the circuit of FIGURE 8 principally concerned with calculating the range of the target point,

FIGURE 10 is a more detailed illustration of the portion of the circuit of FIGURE 8 principally concerned with calculating the elevation of the target point and providing certain parameters to the range and azimuth portions.

FIGURE 11 is a more detailed illustration of another portion of the circuit of FIGURE 8 principally concerned with calculating the azimuth of the target point,

FIGURE 12 is a detailed illustration of the portion of the circuit provided to display the information in the most conveniently usable form,

FIGURE 13 is a diagrammatic representation of the radar operators screen showing markings thereon, and

FIGURE 14 is a diagram of a computing mechanism for deriving the desired values for the necessary correction of the friendly fire.

Overall system (FIGURE 1) FIGURE 1 shows the radar system RD mounted on a vehicle V being used to observe the trajectory T of a projectile fired by a mortar positioned out of direct visual or radar range behind hills H. The antenna system of the radar system RD provides a narrow beam substantially circular in cross-section having a width of approximately 16 mils (approximately 1, a mil being 360/6400) in both directions. The system causes this narrow beam to scan horizontally through approximately 400 mils (22.5) alternately in two planes P1 and P2 separated in angle by approximately mils (2.25) at beam centres. This action defines, by the narrow beam locus, two vertically superposed fan-shaped beams, each scanned 20 times per second, hereinafter referred to as the upper and lower beams. This eifect is achieved by use of a Foster type scanner SC similar to that disclosed in Foster US. Patent No. 2,832,936 issued April 29, 1958, and moditied to provide a dual beam in a manner similar to that described in Mobile Radar Pinpoints Enemy Mortar Positions, by M. S. Jattee et al. Electronics," September 18, 1959, page 34 et seq. The scanner SC is placed at the focus of a semiparabolic cylinder RF which reflects two focused beams. The scanner SC and reflector RF are mounted as an assembly on an antenna platform AP on the vehicle V, which platform is maintained horizontal at all times (see United States patent application No. 269,363 filed April 1, 1963). The scanner-reflector assembly can be inclined relative to this horizontal platform AP to alter the angle of sight of the beams as a pair while maintaining constant their angular separation. The limits of this adjustment may for practical purposes be set at 212 mils (12) above the horizontal to 106 mils (6) below the horizontal, these angles being between the lower beam plane P2. The antenna assembly can be rotated to provide complete radar coverage throughout 6400 mils (360) in azimuth.

Mathematics 0 the computations to be made (FIGURES 2 I0 5 Before considering the detailed nature of the display which appears on the radar screen as a result of a projectile passing through the upper and lower beams, it is necessary to consider the mathematics of the problem, taking as a first assumption that the echoes received from each beam can be resolved into a single point on the trajectory T of the projectile, the range and azimuth of which point thus becomes known. The angle of sight (0) of the lower beam to the horizontal is known by the setting applied to the scanner-reflector assembly by the operator. In practice, the operator will make this angle of sight as small as he may having regard to the limitations of the terrain. He will normally aim the antenna so that the lower beam just clears the treetops, or other high point, such as the upper outline of the hills H in FIGURE 1. He may be provided with a telescope aligned with the lower beam to facilitate this setting.

FIGURE 2 shows two intercept points a and b on trajectory T determined by the radar system RD at ranges R1 and R2 respectively, it being assumed for simplicity in this first diagram that the trajectory T is directed straight towards the radar system RD with no change in azimuth between points a and b. The angle of sight of the lower beam is shown as 0, and the fixed angle between the two beams is designated a. The angle represents the difference between the horizontal plane HP through the radar system RD and the working plane WP which is the plane in which both the radar system RD and the target point lie. The target point will be assumed to be occupied by an enemy mortar for the present description. The mortar is in fact positioned at the point M which is the extrapolation of the trajectory T from points a and b to the working plane WP, asseming the trajectory to be substantially parabolic. Point M would be the position of the mortar if it were on the horizontal plane HP, and points f and f are the corresponding points on the horizontal and the working planes for a straight line extrapolation from points a and b.

It will be appreciated that the angles at which the radar system is working in practice will be very small compared with the angles actually shown in FIGURE 1. It is necessary to exaggerate the size of the angles in FIG- URE 1 in order to have a workable diagram. With this point in mind it will be appreciated that many of the approximations employed in the subsequent calculations are in fact a good deal closer to being true than would at first sight appear from FIGURE 1, by reason of the fact that such small angles are encountered in practice.

Consider first the straight line extrapolation back from points a and b to point Since triangle ban is similar to triangle aef Now, remembering that the angles are small, the following approximations can be made.

dwRlB bc Rza Rlot 0 and a being expressed in radians.

Thus

R10 7 6f -m AR-IXAR This function thus represents the correction for straight line extrapolation, where K= =a constant times 0 and thus varies with that angle.

As above indicated, the working plane WP is provided to take care of the situation occurring when the position of the mortar M is above or below that of the radar system RD, e.g. at M. An estimated working plane is initially assumed by the operator as a rough calculation from a contour map, since he knows the general location of the mortar, and is later corrected as required in a manner to be described below. The operators initial estimate of the working plane angle radians does not affect the angle of sight 6 of the radars lower beam; it merely plays a part in the calculations.

Taking the working plane WP into account efz% AR KAR where K now equals namely a constant times (9+q5).

The mortar range Rm has now been found as R1+KAR.

FIGURE 2 assumes that the mortar is firing directly towards the radar system RD. FIGURES 3 and 4 have been constructed with a different assumption, namely that the mortar is firing exactly at right angles to the line of sight from the radar system RD. Under these conditions there is a change in azimuth, but no change in range, between the two detected projectile intercepts a and b. Al and A2 (FIGURES 3 and 4) are assumed to be the azimuth angles in radians from a convenient datum (such as North) of the detected points a and b.

As FIGURE 4 shows cam (AlA2)R=-AA R, where R=RI=R2.

Also

GG-R6 and bCRzRtZ where 0 and a have the meanings already ascribed to them. Consequently ef eKAA R where as before.

The mortar azimuth Am has now been found as A 1 +KAA If the mortar is not firing directly towards the radar system RD or on a line perpendicular to it, but at some angle in between, the same diagrams will apply for the components, and in the general case there will be both AR and AA factors for each trajectory. To visualize AR, the trajectory and its intercepts may be visualized as projected on a vertical plane (AR plane) passing through the radar system and mortar, and to visualize AA, a similar projection may be made on a plane (AA plane) at right angles to the radar-mortar line. In each case, the trajectory will be fore-shortened by the cosine of the angle between the trajectory plane and the plane on which the projection is made. The mortar is located on the ground in polar coordinates to a first approximation as R1+KAR; Al-i-KAA. The computer can thus determine the mortar position by storing the information RI and Al, calculating AR and AA from information set in by the operator, and performing the necessary multi plications and additions to obtain the desired result.

The foregoing calculations have been based on a straight line extrapolation and will result in quantities KAR and KAA which are too great and tend to overshoot the actual mortar position, due primarily to the parabolic nature of the actual trajectory T. In other words, the calculations approximately find point f instead of point M. Due to the assumption that the distance ac in FIG- URE 2 is equal to the difference in range Rl-R2=AR (which assumption is not entirely true), the overshoot error arrived at by assuming a straight line extrapolation is somewhat reduced, at least as far as range is concerned. It is not reduced in azimuth since the assumption just mentioned forms no part of the geometry of FIGURE 3. Indeed, at certain angles of sight and angles of mortar fire, the point 1" (as calculated by using the multiplication KAR as explained) can even lie between the mortar M and the radar system RD in FIGURE 2.

The distance Mf' (or Mf) may be found in terms of the parameters of a typical parabolic trajectory with reference to FIGURE 5, Dr being the directix of the parabola, and p being the semi-latus rectum.

For any parabola S=2ph.

Also V the velocity of the projectile in the x direction at point a, is equal to the distance travelled, x, divided by the time taken. The projectile is assumed to be subject to gravity only, and the horizontal component of the velocity to be constant.

Thus:

Squaring and dividing throughout by g, the gravitational constant, gives Vat m Now it is also known from the geometry of a parabola that the time taken for a projectile to reach the vertex, t is given by the expression When x=S and 1 1 which occurs at the vertex, from the combination of the foregoing equations The vertical component V of the projectile velocity at point a is given by the well known expression for a parabolic trajectory ya y) If new the equation S :l.ph is expanded for any point on the parabola, it becomes with the sign representing an imaginary case.

The distance L shown in FIGURE 5 is given by the geometry of the system from the relationship and using the above expression for x gives If we now substitute in this equation the expressions for V and vya: We get 9 may...

Now, in the AR plane,

Ee AT where AT is the time between intercepts.

Also x=K'AR, Where K is the corrected value of K to obtain the true mortar position.

Substituting, we get 9 (K'AR) 9 Since the variables V and V Will be found not at point "a but at a point halt-way between a and b (see FIGURES 2 to 4) the quantity K should read K'+ 1 2.

The reason for this is that K is the corrected value of K which latter should really be for a point mid-way between points a and b. This expression K+%( K corrected) It should be remembered that K and K are pure (dimensionless) numbers.

The equation to be solved becomes then 8 K=K-Q Taking g=9.8 meters/sec.

a==40 mils=0.03925 radians -L afzxnsszrf This constant is used in conjunction with other constants of the mechanical gearing described below in determining the correction to be applied as a shaft rotation.

In the AA plane (FIGURE 3) a. similar procedure may be used.

and

RAA AT then Etch/ ERM Ra approximations were made. For example in FKGURE 3 (AA plane) cazAA XR aezRIO bC Rzqfu In FIGURE 2 is it apparent that the greater part of the error is due to the approximation where the distance as is the actual AR and ca: cu+ ua The distance cu can be approximately determined by ordinary trigonometry as cu za (whg) Rm Where Rm is the range from the radar system RD to the mortar M.

This equation is derived from the fact that the distance bs is given by the well known expression bs=2R2 sin 5 Since the angle between the line lbs and the line cb is equal to then cuzbs sin (6+3) -2R2 sin 3 sin (6+ z R ma Taking oc==40 mils, and Rm in meters, and 9 in mils, this equation becomes N fH-ZO) Rm N 25,840

Thus the true target (mortar) position in polar coordinates from the radar system RD, where Am is the angle between North and the line of sight to the target, are given by equations These equations have been designated Equations 1, 2 and 3 respectively for ease of subsequent reference to them. It should be pointed out that, in applying the above equations, account must be taken of the sign of AA and AR. If A2 is clockwise from Al, AA is negative; and, if the mortar is firing away from the radar, AR is negative.

The true target position has thus been determined in polar coordinates Rm and Am, and it remains only to convert to rectangular (cartesian) coordinates. This is done by means of a resolver, the output of which is Rm sine Am and Rm cosine Am If the radar position is added to these quantities as Eastings and Northings then Rm sine Am-t-Radar Eastings=Target Eastings Rm cosine Am-i-Radar Northings=Target Northings Besides determining the target position in plan, the computer will provide an elevation (in feet above sea level) of this position. This is necessary for the operator to determine the correct angle at of the Working plane WP. The elevation of the target relative to the radar is Rm sine but for simplicity, and because 5 is always small, this is taken as Rmqb. With being measured downwards from the horizontal, the equation for elevation becomes -Rm+Radar Elevation=Target Elevation The manner of use of this information by the operator is described below.

Nature of echo presentation and operators procedure (FIGURES 6 and 7) Attention is now directed to FIGURE 60, b and 0. FIGURE 6a shows a plan view of a typical sector SR scanned by the radar RD. Two composite echo displays E and E produced by the lower and upper beams, respectively, are shown. FIGURE 6b demonstrates the manner in which the sector SR is presented on the screen S of a B-scope, that is to say a scope which exhibits azimuth along the horizontal axis and range along the vertical axis. After having detected a weapon firing, the operator will enlarge the critical area of the sweep as demonstrated by FIGURE 6c.

The echo displays actually received in practice are 10 more complex than those illustrated in FIGURES 6a, b and c, and attention is now transferred to FIGURES 7a to f for a more detailed discussion of the nature of the display on the screen actually observed by the operator.

As a projectile enters the field of scan of the lower beam, an echo E1 is displayed on the screen S by a group of individual signal returns resulting from a single passage of the narrow beam across the projectile. The center of the leading (lower) edge of this echo (point C1) represents the true position of the object (projectile) being observed. As the beam continues to sweep, a series of such echoes appears on the screen S. These echoes are indicated as E1 to E5 in FIGURE 7b and make up the composite echo E of FIGURES 6a to c. In reality there may be many more than five individual echoes in this series. Echoes E1 to B4 are shown in bro-ken lines because some fading will have taken place by the time the last echo E5 appears. The duty of the operator is to observe or mark the center points C1 and C5 of the leading edges of the first and last echoes and to estimate the mean point CML between these two extreme center points. The screen S is provided with an outer surface that can readily be marked by the operator using a suitable stylus. He may mark points C1 and C5 on the screen as echoes E1 and E5 appear, and then estimate and mark the mean point CML, but an experienced operator will be able to estimate quite closely the mean point CML and mark it on the screen merely by observation of the series of echoes, without finding it necessary to go through the preliminary stage of actually marking points C1 and C5. The vital point to obtain as accurately as possible for the purposes of subsequent operation of the computer is the mean point CML of the centres of the leading edges of the series of echoes LR resulting from the lower beam.

Assuming that the mortar is firing from left to right and towards the radar system RD, the sccond series of echoes UR detected by the upper beam and shown as composite echo E in FIGURES 6a to c appears first as an echo E6 (FIGURE 7c) and continues down to echo Eli (FIGURE 7d). These echoes of the second series will similarly have leading edge center points C6 to C10, the mean point of which is designated CMU. The upper beam echoes will appear in a lower position on the screen S than the lower beam echoes when the mortar is firing towards the radar, since the range will have shortened somewhat by the time the projectile reaches the upper beam.

Thus, by the time all the echoes have faded from the screen 5, the operator will have marked at least the points CML and CMU. which points represent the mean positions of the projectile as it passed through the lower and upper beams respectively. It has been found in practice that a skilled operator can access the positions CML and CMU to an acceptable degree of accuracy even though estimating these po1nts requires visual and manual dexterity.

As well as carrying out the functions just described. the operator will time the interval the projectile takes to pass from the lower to the upper beam. He can do this either by comparing the first echo of each beam, the last echo of each beam or any pair of corresponding points on the two beams. It has been assumed in FIG URE 7 that he uses the first method and records the time between the respective first echoes E1 and E6 of the lower and upper echo series LR and UR. For this purpose, the operator has a hand switch HS situated beside the screen S. A right-handed operator will push the switch HS with his left hand, to leave his right hand free for marking the screen S. A second, parallel operating, hand switch H5 is provided for left-handed operators. As FIGURE 7:: indicates by an arrow, the operator will push in the switch HS immediately on appearance of the first echo E1 of the lower beam. This operation will start the timer TM. When the first echo E6 of the 11 upper beam appears (FIGURE 70) the operator will again push the hand switch HS to stop timer TM which will now remain in its new position indicating AT, the time of travel from the lower to the upper beam by the projectile.

As FIGURE 7e demonstrates, the operator is left, after passage of a proiectile, with two points CML and CMU marked on his screen S, and AT recorded in the timer TM.

The screen S is also provided with a marker spot MS, which is an electronic marker produced by conventional circuitry in the radar transmitter-receiver combination and synchronised with the scope sweep so as to occupy a single desired position on the screen S determined horizontally by an azimuth marker handwheel AMH and vertically by a range marker handwheel RMH. Referonce may be made to E. F. V. Robinson Canadian Patent No. 588,247 issued July 28, 1959, for a description of a system for achieving this result. The operator first moves the marker spot MS by means of the handwheels AMH and RMH to coincide with the point CML and when he has achieved this coincidence he presses a foot switch PS (FIGURE 72). Depression of switch FS brings the computer into full operation, as will appear in more detail below. Although illustrated simply, the switch FS is a toggle switch of the type commonly employed to raise and lower the headlights of an automobile, that is to say a switch which remains in each acquired position until reactivated by a further depression of the operators foot to be reversed. As demonstrated by FIGURE 7 after closing switch FS the operator moves the marker spot MS with handwheels AMH and RMH to the point CMU, while switch FS remains closed. In this way, the operator feeds into the computer the difference in range AR and the difference in azimuth AA between these two points.

Operation of the computer (FIGURES 8 to 12) For an understanding of the manner in which the target point is calculated from the information available, reference will now be made to FIGURES 8 to 12.

FIGURE 8 shows as a single block RDR a radar transmitter and receiver assembly with related circuits for the B-scope and the electronic marker spot MS. These circuits are conventional and their particular nature forms no part of the present invention. Assembly RDR is coupled electrically and mechanically to the antenna ANT comprising the scanner-reflector assembly already described.

The computer portion of the circuitry which the re- The range circuit portion (FIGURE 9) The range marker handwheel RMH previously described in connection with FIGURE 7 controls movement of the marker spot MS on the screen 8 in the range direction through a goniometer assembly G1 to which its rotation is transmitted by shaft Ht. Goniometer assembly G1 controls the range position of the marker spot MS on the screen. it also, through shaft H4, operates a cam CAM7 which controls a pulse repetition frequency switch PRFS. This switch changes over the radar systern from short to long range.

At the same time the handwhccl motion is transmitted by shaft H1 to a first input of a mechanical differential D1. Thus, when the marker spot MS is moved to the point CML in FIGURE 70, the range R1 of such point is fed into the differential D1. As already explained, once the marker spot MS has been aligned with point CML, the operator operates foot switch FS which remains closed. As shown in FIGURE 9, foot switch FS serves to energize a mechanical clutch CL2 which now connects the shaft H1 of the handwhcel RMH to shaft H3 which forms another input to differential D1 acting in opposition to shaft H1. As a result, when the marker spot MS is moved by the operator towards point CMU (FIGURE 7 the output of differential D1, shaft H2, remains stationary since AR (the range dilference between points CML and CMU) is being inserted twice in opposite senses into diiferential D1. The position of shaft H2 represents the range value R1, while shaft H3 is moved a distance equal to AR.

Foot switch FS energizes relay RY, one pair of contacts RYl of which is opened to deenergize a clutch (11 which had hitherto been holding shaft H3 under the control of a motor M1. Contacts RY2 which are closed by energization of the relay RY serve to ground the input to a motor return amplifier MR1 deenergizing motor M1. The zeroing function of this motor M1 will be described below in connection with the resetting of the system.

The factor -AR is transmitted by shaft H3 to a movable slidcr on a resistor RRZ. This part of the circuit is concerned with simulating Equation 1 above, which for convenience is here repeated.

Rm=121+K'[AR+a(e+)Rm] (i) If the last term is called I, this equation becomes And if numerical values are inserted, this equation becomes I (6+20)Rm] Rm 1a1+rt [s1z+ (1b) The factor J is added to AR by means of resistors RRS and RR9 arranged in series with resistor RR2. Resistors RRS and RR9 each have a movable slider controlled through a shaft H6 by a motor M2 which is made to turn by an amount representing the factor J, as will now be explained. By definition J is equal to the angle of sight 0 plus a constant, multiplied by the range Rm, all divided by a further constant. The range Rm is inserted by a shaft H9 controlling a slider on a resistor RRS, and a (the angle of sight) is inserted by a shaft Hi0 controlling a slider on a resistor RR6. The constant is added to 0 by choice of the initial position. Movement of shaft H19 is controlled by the elevation circuit portion shown in FIGURE 10 and described below. A relay RZ shown in FEGURE 10 controls contacts R21 and R22 to close the former and open the latter after hand switch HS and foot switch FS have been actuated. Closure of contacts RZI connects the resistor RRS to the input of a servo-amplifier SAl to impose thereon a voltage representative of the produce of the positions of the sliders on resistors RRS and RR6, namely Rm (6+a constant). Servo-amplifier SAl energizes motor M2 to drive its shaft Had to reorient the position of a grounded slider on a resistor RR'I' in such a way as to restore the input to the amplifier SAl to zero. This servo-loop thus maintains the shaft H6 at all times at a position representative of the function J, the constant in the denominator of this expression being provided by the mechanical ratio between shafts H6 and Hen.

As noted above, shaft H6 is connected to the movable sliders on resistors RR8 and R119 whereby the combination of these resistors with resistor RRZ generates the function Ali-H.

It is now necessary to form the product of such latter function and the function K. The function K is inserted into the system of FIGURE 9 at the slider of a resistor RR3 by a shaft H7 the position of which is controlled in the manner subsequently described in connection with FIGURE If). Resistor RR3 is series connected with the slider on resistor RRZ by contacts RYS which are closed when relay RY is closed and the resulting produce output is connected through closcd relay contacts RY4 to a servo-amplifier SA2 which controls a motor M3 the shaft H8 of which moves a grounded slider on a resistor RRl in a manner to restore the input of amplifier SA2 to zero. These parts thus form a second servo-loop whereby the shaft H8 is maintained at all times in an angular position corresponding to the function K(AR +1) A second differential D2 receives input from shafts H2 and H8 to form the sum of R1 and K(AR+J), which sum is Rm in accordance with Equation 1a. The function Rm appears at the output of differential D2, shaft 1-19, to be fed into target range counter CTl which indicates the target range. Shaft H9 also moves sliders on resistors RRtl and RR15 for reasons that will appear when FIGURE 10 is considered, moves a slider on a resistor RRltl for a reason that will appear when FIG- URE 12 is considered, transmits the Rm function to the slider of resistor RRS for generation of the 1 function in the manner already described, and operates a cam CAMtS which actuates range change-over switches RCSI and RCSZ which change the computer over from short range to long range by altering the supply point of power to resistor RRltl and its preset balancing resistors RRltla and RRltlb.

When foot switch FS is reversed to de -energize relay RY, contacts RY10 close to apply the return signal to servo-amplifier SA2 which causes motor M3 to center the slider on resistor RRl. Contacts RYl also close to energize clutch CLI to connect shaft H3 (clutch -CL2 now being de-energizcd) to motor M1 for return to zero position under the control of: motor return amplifier MRI which is now connected through contacts RYll to the slider of resistor RR2. The slider of this AR resistor RRZ is thus returned to center position through the zeroing of shaft H3. Contacts RY4 cause motor M3 to return the slider of resistor RRl to center position. These two potentiometers will then remain in this position until a new problem is set in and the foot switch FS is again pressed to close relay RY.

The elevation circuit portion (FIGURE 10) Turning now to FIGURE 10, the angle of sight of the antenna ANT is fed to the computer from a synchrotransmitter ST geared to the antenna. This information concerning the value of 0 is applied to the stator of a control transformer B3 and develops an error voltage in its rotor, which voltage is applied as an input signal to a servo-amplifier SAS controlling a motor M4, the output shaft H of which turns the rotor of control transformer B3 to cancel out the error voltage and thus complete the servo-loop. Shaft H10 also controls the slider on resistor RR6 as already described in FIGURE 9, feeds to an angle of sight indicator I1, and is applied as an input to a dilferential D3.

As already explained, the operator commences by estimating the working plane WP from a contour map and by setting such estimate of the angle at on a working plane handwheel WPH, The shaft H11 of handwheel WPH transmits motion to a working plane indicator 12, as well as to a second input of differential D3 and to the slider of resistor RRIS. The output of differential D3 is a shaft H12 which thus represents the factor (H-o). By adjustment of the gear ratio this factor can be divided by a constant to derive the factor K which equals 14 a being a constant. Shaft H12 thus feeds K as an input to another differential D4 where the factor K is derived by subtracting the function Q from K. See Equation 3 above.

a 2aRm The output of differential D4 (representing K) is applied to shaft H7 which, as already indicated, is fed to the slider of resistor RR3 in FIGURE 9. It is also fed to the slider of a resistor RR21 of the azimuth portion of the circuit to be described in connection with FIG- URE 11, and to the slider of a resistor RR12 of a circuit now to be described.

The factor Q applied to differential D4 by shaft H13 is derived in another servo-loop formed as a bridge. The inputs are factor Rm at resistor RRll (from FIG- URE 9), factor K at resistor RR12 (which resistor by virtue of additional end turns is made to represent the function Kl /z), and AT, the time function, at resistor RR13. (Derivation of factor AT will be explained below.) Servo-amplifier SA4 monitors the output of the bridge and controls a motor M5 to restore equilibrium by move ment of the slider of a resistor RR14 forming the fourth arm of the bridge. The position of motor M5 is also transmitted by shaft Hi3 to differential D4. The resistors EH12 and RR13 at which factors K+ /2 and AT are inserted are wound as square law potentiometers. Resistors RR and RRM are linear. By appropriate adjustntcnt of the constants, the factor Q is obtained at shaft Hi3 equal to ill) r Servohmpliticr SA is cam controlled through contacts CCl from the AT circuit, so this servo-loop can only function when AT has been set into the computer.

The AT circuit (FIGURE ltl) operates as follows. Motor M6 is a continuously running synchronous motor and its shaft H14 can be connected to shaft H15 con trolling resistor RRI3 and cams (AMI and CAM2 by means of a clutch GL3. Clutch GL3 is energized through contacts RXl of. a latch relay RX controlled by hand switches HS and HS previously described in connection with FIGURE The relay RX is of a type which latches alternately in and out upon subsequent energizations. Upon being latched in by initial actuation of say switch HS as demonstrated in FIGURE 7a, contacts RXl are closcd to energize clutch CL3 and transmit the rotation of the motor M6 to shaft H15 thus beginning to count the factor AT on timer TM. Indicating lamp LPZ is de-energized at this time by opening of contacts RXZ.

As soon as shaft H15 starts to turn, earn CAMl closes contacts CCl to permit the servo-loop of servo-amplifier 8A4 to operate, and cam CAM2 opens its contacts CCZ and closes its contacts CCS. Assuming that hand switch HS or H5 is again actuated by the operator before cams CAM] and CAMZ and timer TM have completed one full rotation (as in FIGURE 7c), contacts CCl, CC'Z and CC3 remain in their new positions when, upon the second closing of switch HS or HS, the relay RX is returned to its initial position to de-encrgize clutch GL3 leave shaft H15 in the position it has acquired representing the factor AT. With this AT information thus stored in shaft H15, as soon as the foot switch FS is closed (FIGURE 72) a circuit is completed through closed contacts CC3 to energize a relay RZ which closes contacts R21 and opens contacts R22 in the circuit generating the J function (see FIGURE 9). At the same time indicating lamp LPl is lit. In this way the J function can only be applied when the AT factor has been set in and the foot switch FS is in the actuated position. However, if the projectile is known to be of the type having a straight line traiectory such as a selfpropcllctl rocket, it is possible to retain the J function while removing the Q factor from the equations. This effect is achieved by closing a rocket switch ROC which short circuits the active portion of resistor R1113. The result is an approximately straight line extrapolation, the most appropriate for this type of projectile.

Another part of the circuit shown in FIGURE 10 is that derived from the shaft H11 of the Working plane handwheel WPH to control the position of a slider on a resistor RRIS. This part of the circuit is designed to derive the elevation, which is a function of the working plane angle o and of the range Rm which is applied by movement of a slider on a resistor RR16 (FIGURE 9). This is another servo-loop consisting of a servo-amplifier SAS controlling motor M7, the output shaft H17 of which adjusts resistor RRIT to restore the input of amplitier SAS to zero while the output from shaft H17 is also fed to another differential D5. The known elevation of the radar system is applied at radar elevation handwhcel RLH and is fed by shaft Hi6 to appear directly in counter GT while being added in differential D5 to the difference in elevation between the radar system and the target, Rmp, as determined by the chosen working plane, to give the elevation of the target in shaft H5 and counter GT4.

In operation, once the operator has a first reading of the target point, he checks to see if the elevation appearing in counter GT4 agrees with the elevation shown on his map of the target location. If it does not, he turns the working plane handwheel WRH until the counter GT4 shows the elevation given by the map at the target location as determined by the computer. This adjustment is automatically applied to all the other dependent variables in the system and a new location is immediately computed. The operator then rccheclts the map elevation and makes a further adjustment if necessary (normally only one resetting is required).

The azimuth circuit portion (FIGURE 1]) We come now to consideration of the manner of determining azimuth, for which purpose reference should be made to FIGURE 11. Information concerning the antenna azimuth AA is supplied to the computer by an assembly consisting of two synchro-transmitters 5T2 and ST one geared directly to antenna azimuth rotation and the other (Vernier) rotating 15 times per antenna rotation. This synchro information is applied to the stator of respective main and vernier control transformers 4 and B5. Since these rotors are not free to turn. an error voltage is developed in one or both rotors if they are not aligned with the actual antenna position. These error voltages are applied to a signal selector SS which receives inputs from the rotors of both the main and vernier transformers B4 and B5. As soon as the input from the main control transformer B4 is above a specific voltage level than this error signal controls the output of the signal selector SS. When the error signal from transformer B4 drops below this level, i.e. approaches a null, then any signal being developed by the vernier control transformer B5 becomes the controlling voltage and is passed by the signal selector SS. The output of signal selector SS passes to a servo-amplifier SAG, and the servo-loop is completed by a motor M8, the shaft H18 of which is connected to the rotors of transformers B4 and B5. Motor M8 thus drives the control transformers to their correct nulls. Should the main control transformer B4 reach its wrong null, i.e. 3,200 mils out, then the controlling voltage from the vcrnier control transformer B5 will drive the servo away from this null towards the correct one, so that the system will only stabilize itself on the correct azimuth setting.

Shaft H18 of motor M8 also drives through a differential D6 to appear on an antenna azimuth counter CTS via shaft H19, which also transmits this motion through a differential D7 to a shaft H and a target azimuth counter GT6. An azimuth orient handwheel AOH controls a shaft H21 also feeding into differential D6. In setting up, this handwheel AOH is rotated until the antenna azimuth counter CTS reads the correct bearing of the center of scan of the antenna to a known target. In this way the antenna azimuth is oriented in respect to a compass hearing such as North. Shaft H21 is then locked by lock LKl.

Shaft H19 also feeds into a further differential D8 which receives a second input from the azimuth marker handwheel AMH via shaft H21. The output of differential D8 is recorded in an antenna-i-marker counter CT7. An azimuth potentiometer AZP controlled by shaft H21 controls the position of the marker spot MS in azimuth on the screen S. In addition to driving differential D8 the azimuth marker handwheel AMH also drives differential D9, a imarker counter GT8, and one side of a clutch CL4.

Differential D9 may be considered as .a storage device. It functions so as to have an output which indicates the position of the marker spot MS at the first intercept point CML. When the marker spot MS is aligned with point CML (FIGURE 7e) the foot switch FS is closed to energize clutch CL4 so that any further motion of the azimuth marker handwheel AMH is applied both directly to differential D9 by shaft H21, and in opposite sign to the same differential through clutch CL4 and shaft H22. Such applications thus subtract from one another. Differential D9 effectively stores the azimuth position of the marker spot MS at the point CML, namely A1, and passes this information on through shaft H23 to differential D10.

Shaft H22 which only starts to turn after foot switch FS closes clutch CL4 thus provides a measure of AA, the difference in azimuth, and this function is transmitted to a slider on a resistor RR21 of a further servo-loop designed to provide the multiple KAA. The factor K is inserted at the slider of resistor RR21 being obtained from shaft H7 of the FIGURE 10 circuit. Resistor RR21 is series connected by contacts RY7 of relay RY (when energized by foot switch FS) with the slider of resistor RR20. The output which traverses now closed contacts RY8 appears at the input of servo-amplifier SA7 to control the position of motor M9 which in turn controls the slider of a resistor RR22 through shaft H25 in a manner to restore the circuit to balance.

The position of shaft H25 then represents the function K'AA which is applied at differential D10 to be added to factor A1 and hence transmitted through shaft H24 to be added in differential D7 to the antenna azimuth to provide an output in shaft H20 which represents target azimuth, Am. See Equation 2, AM=A1+K'AA. This value Am appears in target azimuth counter CT6 and is also fed to a resolver RS shown in more detail in FIG- URE 12.

When foot switch FS is reversed to de-energize relay RY, contacts RY9 close to apply the return signal to servoamplifier SA7 which causes motor M9 to center the slider on resistor RR22. Contacts RYS also close to energize clutch CLS to connect shaft H22 (clutch CL4 now being de-energized) to motor M10 for return to zero position under the control of motor return amplifier MR2 which is now connected through contacts RY12 to the slider on resistor RR20. The slider of the AA resistor RR20 is thus returned to center position through the zeroing of shaft H22. Contacts RY9 closing causes motor M9 to return the slider of resistor RR22 to center position. These two potentiometers will then remain in this position until a new problem is set in and the foot switch FS is again pressed to close relay RY.

When echoes appear too close to the edge of the screen S, a centering device incorporated in the circuit portion of FIGURE 11 allows the centering of the radar scan on the position of these echoes. The amount and direction of rotation of the antenna may be initially determined by the azimuth marker spot setting or approximated by the operator and set on centering dial CD through shaft H26 by azimuth centering knob ACK. Clutch CL6 and the antenna relays are de-energized while knob ACK is being turned, but operate as soon as torque is removed from the centering knob. Shaft H26 also controls cams CAM3 and CAM4 which respectively operate clockwise antenna rotation switch CWS and counter-clockwise antenna rotation switch CCWS. These switches control the antenna ANT so that it will rotate automatically in the direction and the amount set on dial CD.

As a second embodiment of this azimuth centering device (not illustrated), the cams CAM3 and CAM4 are both attached to shaft H21 instead of shaft H20. A suitable clutch arrangement is then provided coupling the antenna azimuth shaft H18 to the shaft H21. A manual switch provides excitation for this clutch arrangement as well as for switches CWS and CCWS which remain mechanically actuated by cams CAM3 and CAM4 to cause the antenna to rotate automatically until the marker spot displacement is removed. This thus constitutes a fully automatic azimuth centering device.

The information circuit portion (FIGURE 12) FIGURE 12 shows the information portion of the system which is provided to convert the target ranges and azimuths to Eastings and Northings. This i accomplished by obtaining a voltage proportional to target range Rm from resistor RR (see also FIGURE 9) and applying this voltage to the stator RSS of the resolver RS through a booster amplifier BA, while the rotor RSR of the resolver RS is rotated in proportion to the target azimuth Am obtained from the shaft H of FIGURE 11. The outputs of the windings of the resolver rotor RSR are then proportional to Rm sine Am for Eastings and Rm cosine Am for Northings, such Eastings and Northings being the relative Eastings and Northings of the target in relation to the radar system. Amplifier AR3 and motor M12 form a servo-loop for the Eastings with an output in shaft H which drives a slider on resistor RR30 until its voltage is exactly equal and opposite to that generated in the rotor winding of resolver RS to which such slider is connected. Similarly, amplifier AR2 and motor M13 form a servo-loop for the Northings giving an output in shaft H31 driving the slider of resistor RR31. Resistors RR30 and RR31 are supplied with power from points W, X, Y and Z as indicated from FIGURE 9. A differential D12 driven by shaft H30 has the known radar Eastings applied to it by radar Eastings handwheel REH and shaft H32. A differential D13 driven by shaft H31 has the known radar Northings applied to it by radar Northings handwheel RNH and shaft H34. Absolute radar Eastings appears in counter CT9, while the sum of shafts H30 and H32 appears in shaft H33 as the target Eastings (that is the absolute target Hastings) and is displayed in counter CT10. In a similar manner, absolute radar Northings appears in counter CTll, while the sum of shafts H31 and H34 appears in shaft H35 as the target Northings (that is absolute target Northings) and is displayed in counter CT12. Shafts H32 and H34 are normally clamped by locks LK2 and LK3.

Correction of fire mechanism (FIGURE 14) As described in connection with FIGURE 7b, the operator, having observed a first series of echoes of an enemy projectile, estimates visually and marks on the screen S a mean center point CML for the lower beam. This point has been designated CMLE in FIGURE 13, and the mean point for the upper beam intercept of the enemy projectile has been designated CMUE. The computer calculates an extrapolation from these points down the trajectory of the projectile to determine the position of the enemy weapon (target point) and displays this information on a number of counters, both in polar coordinates from the radar system (counters CTl and GT6) and in map Eastings and Northings (counters CT10 and CTIZ),

information concerning the Eastings and Northings of the radar system itself having been supplied to the computer. This target point is not displayed on the screen, but has been shown as point EXE in FIGURE 13 for explanatory purposes.

In order to use the particular facility herein described, the operator resets the correction of fire mechanism to zero by means of control knobs C141 and CKZ and closes the correction of fire switch CPS. The control knobs CKl and CK2 are push-to-engage knobs which, when pushed, drive shafts H36 and H37, respectively, for the purpose of setting counters CT13 and CT14 to zero. At the same time knobs CKl and CK2 open switches CKSl and CKSZ to prevent clutches CL7 and CL8 being energized during the reset operation, if the correction of the switch CFS is already closed. Counters CT13 and CT14 are of the add and subtract type, each having two sets of numerals, one to indicate positive values and the other to indicate negative values, depending upon which direction the shaft H36 (or H37) moves from zero.

Closure of correction of fire switch CFS by the operator will energize clutches CL7 and CL8, thus connecting shafts H36 and H33 together, and shafts H37 and H35 together. Shafts H33 and H35 (FIGURE 12) insert the computed values of target Eastings and Northings, respectively, into counters CT10 and CT12. The counters CT13 and CT14 are now locked into the system and set to zero, thereby effectively storing the target point in the computer (point EXE). Any deviations of the values in counters CTIG and CT12 from this first target point, due to subsequent operation of the computer, must appear as differences in counters CT13 and CT14. These latter counters are referred to as the AE and AN counters, since they indicate the differences in Eastings and Northings, respectively, between two target points.

Having thus stored the information about the location of the first target point EXE, the operator shifts his attention to the radar observance of a friendly projectile dircctcd against this target point. This can be observed in a like manner to enemy projectiles, except that the series of echoes from the upper beam now occurs before those of the lower beam. Corresponding friendly fire mean points, CMUF and CMLF will be marked by the operator on the screen 8, and then fed into the computer in the manner described above that is by use of the marker spot controlled by azimuth and range handwheels AMH and RMH, hand switch HS (or HS) for operating timer TM and footswitch P8. In doing this for the friendly projectile, the operator causes the computer automatically to calculate the extrapolated point of impact of the friendly projectile, EXF, which also has been shown on screen S in FIGURE 13 for ease of understanding, although no actual mark will appear or be made at this point. The actual Eastings and Northings of point EXP, which constitutes a second target point, will automatically appear in counters CT10 and CTlZ, and AE and AN, the difference Hastings and Northings between the two target points, will appear in counters CT13 and CT14. This latter information is in the most convenient form for use by the friendly weapons for the correction of their fire.

Should points CML and/or CMU be unavailable or unusable for either or both trajectories, the operator may use another pair of points in the manner described in Clemence et al. United States patent application Serial No. 269,283, filed April 1, 1963.

Until counters CT13 and CT14 are reset by knobs CKl and CKZ, this procedure can be repeated for successive friendly projectiles, without the need to make any adjustments, until a new enemy target point is selected. The AE and AN counters CT13 and CT14 will follow the computer at all times. However, should either of the shafts H33 and H35 endeavour to drive shafts H36, H37 in either direction from zero beyond the physical limits of the counters CT13 and CT14, cam CAM4 or CAMS, as the case may be, will operate its associated switch S4 or S5 

1. A RADAR SYSTEM COMPRISING (A) MEANS FOR EMITTING TWO CLOSELY VERTICALLY SUPERPOSED, MUTUALLY DIVERGENT, GENERALLY HORIZONTAL, EFFECTIVELY CONTINUOUS, UPPER AND LOWER RADAR BEAMS, (B) MEANS FOR DISPLAYING ECHOES RETURNED BY A PROJECTILE TRAVELLING IN EITHER DIRECTION IN A TRAJECTORY INTERSECTING SAID UPPER AND LOWER BEAMS AND FOR DETERMINING RANGE AND AZIMUTH VALUES OF SAID INTERSECTIONS MEASURED FROM THE RADAR SYSTEM IN RELATION TO A KNOWN AZIMUTH DATUM, (C) A COMPUTER, (D) MEANS FOR SUPPLYING THE COMPUTER WITH SAID DETERMINED RANGE AND AZIMUTH VALUES AND WITH THE VALUES OF THE ANGLES EACH OF SAID UPPER AND LOWER BEAMS MAKES WITH THE HORIZONTAL AND WITH THE VALUE OF THE ANGLE A WORKING PLANE MAKES WITH THE HORIZONTAL, (E) SAID COMPUTER INCLUDING MEANS FOR CALCULATING AT LEAST APPROXIMATELY COORDINATES OF A TARGET POINT ON SAID WORKING PLANE THROUGH WHICH SUCH TRAJECTORY EXTENDS, (F) MEANS FOR STORING SAID COORDINATES, (G) AND MEANS FOR DISPLAYING ANY DIFFERENCES BETWEEN SAID STORED COORDINATES AND THE SUBSEQUENTLY DERIVED COORDINATES OF ANOTHER TARGET POINT. 